How to express 'y*log(1+(dx/(ax+by+c)))' and 'log(xy/(ax+by+c))' using CVX

Question: I want to know that how can we express the following expressions using CVX?

where it is confirmed that this is a concave function for x>0, y>0. a, b, c and d are constant values.

It will be really appreciated if someone can address the above notes problem. Thanks!

Hi, lxn. The 1st expression can be reduced to this form

the 2nd expression can be reduced to -log(a/y+b/x+c/(xy)), equivalently, -log(a/y+b/x+c/(e^z)) and z<=logx+logy, which can be further addressed by

I’m very sorry that I still don’t know how to express the two expressions. Can you be more detailed? Many thanks for your kind response. :sob: